Area of an Obtuse Triangle Calculator
The area of an obtuse triangle calculator contains the formulas to count the area of that type of triangle and does it automatically for you.
Area20.333163from sides 6, 7, 8
Area20.333163
Perimeter21
Sides6, 7, 8
Angles46.5675°, 57.91°, 75.5225°
TypeAcute scalene
Inradius1.936492
Circumradius4.131182
Working
| Semi-perimeter s | 10.5 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 20.333163 |
| Height on side a | 2 × area ÷ a = 6.777721 |
| Inradius | area ÷ s = 1.936492 |
| Circumradius | abc ÷ 4·area = 4.131182 |
| Angle sum | 180° (always 180°) |
The formula
Heron: A = √(s(s−a)(s−b)(s−c)) with s = (a+b+c)/2
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.